#include "parks.h"
#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
//#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
os<<"{";
for(auto e:v)os<<e<<",";
return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
os<<t<<" ";
dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
if(i)os<<",";
os<<get<i>(t);
print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
os<<"{";
print_tuple<0,tuple<Args...>,Args...>(os,t);
return os<<"}";
}
template<class t>
void print(t x,int suc=1){
cout<<x;
if(suc==1)
cout<<"\n";
if(suc==2)
cout<<" ";
}
ll read(){
ll i;
cin>>i;
return i;
}
vi readvi(int n,int off=0){
vi v(n);
rep(i,n)v[i]=read()+off;
return v;
}
pi readpi(int off=0){
int a,b;cin>>a>>b;
return pi(a+off,b+off);
}
template<class t,class u>
void print(const pair<t,u>&p,int suc=1){
print(p.a,2);
print(p.b,suc);
}
template<class T>
void print(const vector<T>&v,int suc=1){
rep(i,v.size())
print(v[i],i==int(v.size())-1?suc:2);
}
template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
rep(i,v.size())
print(v[i]+off,i==int(v.size())-1?suc:2);
}
template<class T,size_t N>
void print(const array<T,N>&v,int suc=1){
rep(i,N)
print(v[i],i==int(N)-1?suc:2);
}
string readString(){
string s;
cin>>s;
return s;
}
template<class T>
T sq(const T& t){
return t*t;
}
//#define CAPITAL
void yes(bool ex=true){
#ifdef CAPITAL
cout<<"YES"<<"\n";
#else
cout<<"Yes"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void no(bool ex=true){
#ifdef CAPITAL
cout<<"NO"<<"\n";
#else
cout<<"No"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void possible(bool ex=true){
#ifdef CAPITAL
cout<<"POSSIBLE"<<"\n";
#else
cout<<"Possible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void impossible(bool ex=true){
#ifdef CAPITAL
cout<<"IMPOSSIBLE"<<"\n";
#else
cout<<"Impossible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
constexpr ll ten(int n){
return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
return __builtin_popcount(t);
}
int popcount(ll t){
return __builtin_popcountll(t);
}
bool ispow2(int i){
return i&&(i&-i)==i;
}
ll mask(int i){
return (ll(1)<<i)-1;
}
bool inc(int a,int b,int c){
return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
sort(all(v));
v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
#ifdef LOCAL
static mt19937_64 gen;
#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
return uniform_int_distribution<ll>(l, r)(gen);
}
template<class t>
void myshuffle(vc<t>&a){
rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
return lower_bound(all(v),a)-v.bg;
}
vvc<int> readGraph(int n,int m){
vvc<int> g(n);
rep(i,m){
int a,b;
cin>>a>>b;
//sc.read(a,b);
a--;b--;
g[a].pb(b);
g[b].pb(a);
}
return g;
}
vvc<int> readTree(int n){
return readGraph(n,n-1);
}
//VERIFY: yosupo
//KUPC2017J
//AOJDSL1A
//without rank
struct unionfind{
vi p,s;
int c;
unionfind(int n):p(n,-1),s(n,1),c(n){}
int find(int a){
return p[a]==-1?a:(p[a]=find(p[a]));
}
//set b to a child of a
bool unite(int a,int b){
a=find(a);
b=find(b);
if(a==b)return false;
p[b]=a;
s[a]+=s[b];
c--;
return true;
}
bool same(int a,int b){
return find(a)==find(b);
}
int sz(int a){
return s[find(a)];
}
};
int construct_roads(std::vector<int> xs, std::vector<int> ys){
int n=si(xs);
map<pi,int> z;
rep(i,n){
z[pi(xs[i]/=2,ys[i]/=2)]=i;
}
{
unionfind uf(n);
rep(i,n){
{
pi w(xs[i]+1,ys[i]);
if(z.count(w))uf.unite(i,z[w]);
}
{
pi w(xs[i],ys[i]+1);
if(z.count(w))uf.unite(i,z[w]);
}
}
if(uf.c>1)return 0;
}
map<pi,int> hori;
map<pi,pi> ps;
{
map<int,vi> y2x;
rep(i,n)y2x[ys[i]].pb(xs[i]);
vc<pi> pre;
for(auto [y,tmp]:y2x){
sort(all(tmp));
vc<pi> cur;
{
int prex=-inf;
for(auto x:tmp){
if(prex+1<x){
cur.eb(x,x);
}else{
cur.back().b=x;
}
prex=x;
}
}
int head=0;
for(auto [l,r]:cur){
rng(x,l,r)hori[pi(x,y)]=0;
while(head<si(pre)&&pre[head].b<l)head++;
while(head<si(pre)&&pre[head].a<=r){
int p=max(pre[head].a,l);
int q=min(pre[head].b,r);
int k=si(ps);
ps[pi(p-1,y)]=pi(0,k);
ps[pi(q,y)]=pi(1,k+1);
head++;
}
head--;
chmax(head,0);
}
pre=cur;
}
}
int s=si(ps);
vvc<int> g(s);
rep(i,s)g[i].pb(i^1);
{
pi pre(-inf,-inf);
int preid=-1;
for(auto [pos,info]:ps){
int id=info.b;
if(pre.a==pos.a){
bool ok=true;
rng(y,pre.b,pos.b){
if(hori.count(pi(pos.a,y))==0){
ok=false;
break;
}
}
if(ok){
g[preid].pb(id);
g[id].pb(preid);
}
}
pre=pos;
preid=id;
}
}
vi d(s,-1);
{
auto dfs=[&](auto self,int v,int w)->void{
if(d[v]!=-1){
assert(d[v]==w);
return;
}
d[v]=w;
for(auto to:g[v])self(self,to,w^1);
};
rep(i,s)if(d[i]==-1)dfs(dfs,i,0);
}
unionfind uf(n);
vi ans[4];
set<pi> used;
auto addvert=[&](int x,int y,int k){
assert(z.count(pi(x,y)));
assert(z.count(pi(x,y+1)));
int i=z[pi(x,y)];
int j=z[pi(x,y+1)];
pi w=pi(x*2+k*2-1,y*2+1);
auto [tmp,b]=used.insert(w);
assert(b);
ans[0].pb(i);
ans[1].pb(j);
ans[2].pb(w.a);
ans[3].pb(w.b);
uf.unite(i,j);
};
auto addhori=[&](int x,int y,int k){
assert(z.count(pi(x,y)));
assert(z.count(pi(x+1,y)));
int i=z[pi(x,y)];
int j=z[pi(x+1,y)];
pi w=pi(x*2+1,y*2+k*2-1);
auto [tmp,b]=used.insert(w);
assert(b);
ans[0].pb(i);
ans[1].pb(j);
ans[2].pb(w.a);
ans[3].pb(w.b);
uf.unite(i,j);
};
{
for(auto [pos,info]:ps){
auto [way,id]=info;
if(d[id]){
if(way==0){
addvert(pos.a+1,pos.b-1,0);
}else{
addvert(pos.a,pos.b-1,1);
}
rng(y,pos.b,inf){
auto itr=hori.find(pi(pos.a,y));
if(itr==hori.ed)break;
itr->b=1;
}
}
}
}
for(auto [pos,k]:hori){
addhori(pos.a,pos.b,k);
}
assert(uf.c==1);
build(ans[0],ans[1],ans[2],ans[3]);
return 1;
}
